Comment on "Zero-field Kondo Splitting and Quantum-Critical Transition in Double Quantum Dots"

L. VAUGIER; A. A. ALIGIA; A. M. LOBOS

PHYSICAL REVIEW LETTERS

AMER PHYSICAL SOC

Lugar: New York; Año: 2007 vol. 99 p. 209701 - 209701

0031-9007

In a recent Letter [L. G. G.V. Dias da Silva et al., Phys. Rev. Lett. 97, 096603(2006)], a system containing a noninteracting and a Kondo quantum dot (QD) has been studied. Interesting effects are observed in the spectral density of the Kondo QD $A_{11}(omega)$ due to the nonconstant density of states
$rho_2(omega)$ to which the Kondo QD interacts. For a side-dot configuration, if the width $Delta_2$ of
$rho_2(omega)$ is sufficiently smaller than the Kondo temperature $T_K$, the Kondo peak is split in two. This splitting was found also in a similar model for quantum mirages [A. A. Aligia, Phys. Rev. B 64, 121102(R) (2001)]. In Ref. [L. G. G.V. Dias da Silva et al., Phys. Rev. Lett. 97, 096603(2006)] the splitting is interpreted as due to a decrease in $A_{11}(epsilon_F)$, where $epsilon_F$ is the Fermi energy, to satisfy the Friedel sum rule (FSR). An alternative interpretation, based on interference between noninteracting resonances is in principle unjustified for a highly correlated system. Here we show that the first interpretation is not correct and provide a justification for the second.